Abstract
The Einstein-Cartan theory, which is a slight modification of the general theory of relativity, is almost indistinguishable in its practical consequences from the latter theory. A characteristic spin-spin repulsive interaction which is of some importance at ultraheavy densities, prevents the singularities occurring in the Einstein-Cartan treatment. It is shown how this mechanism of preventing the singularity applies to cosmological models in which the spins of matter are aligned along some symmetry axis. Some exact solutions without singularities of the relevant set of equations are obtained.
Similar content being viewed by others
References
Cartan, É.: 1922,Compt. Rend. (Paris) 174, 593.
Cartan, É.: 1923,Ann. Éc. Norm. Sup. 40, 325.
Einstein, A.: 1917,Sitzungsber. Preuss. Akad. Wiss. Berlin 1, 142.
Ellis, G. F. R.: 1967,J. Mathematical Phys. 8, 1171.
Ellis, G. F. R.: 1971, in R. K. Sachs (ed.),Proceedings Internat. School of Physics ‘E. Fermi’, Course XLVII, General Relativity and Cosmology, Academic Press, New York-London.
Ellis, G. F. R. and MacCallum, M. A. H.: 1969,Comm. Math. Phys. 12, 108.
Friedmann, A.: 1922,Z. Phys. 10, 377.
Friedmann, A.: 1924,Z. Phys. 21, 326.
Geroch, R. P.: 1966,Phys. Rev. Letters 17, 445.
Gödel, K.: 1949,Rev. Mod. Phys. 21, 447.
Harrison, E. R.: 1968,Monthly Notices Roy. Astron. Soc. 140, 281.
Hawking, S. W.: 1966a,Proc. Roy. Soc. London 294A, 511.
Hawking, S. W.: 1966b,Proc. Roy. Soc. London 295A, 490.
Hawking, S. W. and Ellis, G. F. R.: 1973,The Large Scale Structure of Space-time, Cambridge Univ. Press, Cambridge.
Hawking, S. W. and Penrose, R.: 1970,Proc. Roy. Soc. London 314A, 529.
Hehl, F.: 1966,Abhandl. Braunschweig. Wiss. Ges. 18, 98.
Hehl, F. W.: 1973,General Relativity and Gravitation 4, 333.
Hehl, F. W.: 1974,General Relativity and Gravitation 5, 491.
Hehl, F. W. and Von der Heyde, P.: 1973,Ann. Inst. Henri Poincaré A 19, 179.
Hehl, F. W., Von der Heyde, P., and Kerlick, G. D.: 1974,Phys. Rev. D 10, 1066.
Heller, M., Klimek, Z., and Suszycki, L.: 1973,Astrophys. Space Sci. 20, 205.
Jacobs, K. C.: 1968,Astrophys. J. 153, 661.
Jacobs, K. C.: 1969,Astrophys. J. 155, 379.
Kantowski, R.: 1966, Dissertation, Austin, Texas Univ.
Kantowski, R. and Sachs, R. K.: 1966,J. Mathematical Phys. 7, 443.
Kerlick, G. D.: 1973,Astrophys. J. 185, 631.
Kibble, T. W. B.: 1961,J. Mathematical Phys. 2, 212.
Klimek, Z.: 1971,Postepy Astronomii 19, 165 (in Polish).
Kopczyński, W.: 1972,Phys. Letters 39A, 219.
Kopczyński, W.: 1973,Phys. Letters 43A, 63.
Kuchowicz, B.: 1973,A Spin-dependent Geometry of the Universe, Lecture, Internat. School of Cosmology and Gravitation, Erice (Sicily).
Kuchowicz, B.: 1975a,Acta Cosmologica (Krakow)3.
Kuchowicz, B.: 1975b,Acta Phys. Polon. B 6, 173.
Kuchowicz, B.: 1975c,Acta Phys. Polon. B, No. 4.
Kuchowicz, B.: 1975d,The Einstein-Cartan Equations in Astrophysically Interesting Situations, II, in press.
Kuchowicz, B.: 1975e,J. Phys. A. General Math. 8, L29.
McIntosh, C. B. G.: 1968a,Monthly Notices Roy. Astron. Soc. 138, 429.
McIntosh, C. B. G.: 1968b,Monthly Notices Roy. Astron. Soc. 140, 461.
May, T. L. and McVittie, G. C.: 1970,Monthly Notices Roy. Astron. Soc. 148, 407.
May, T. L. and McVittie, G. C.: 1971,Monthly Notices Roy. Astron. Soc. 153, 491.
Misner, C. W., Thorne, K. S., and Wheeler, J. A.: 1973,Gravitation, Freeman and Co., San Francisco.
Sachs, R. K.: 1973, in W. israel (ed.),Relativity, Astrophysics and Cosmology, Proc. Summer School, August 1972, Banff, Alberta, D. Reidel Publ. Co., Dordrecht-Boston.
Sciama, D. W.: 1962, inRecent Developments in General Relativity, Pergamon Press and PWN, Oxford-Warsaw.
Stewart, J. and Hájiček, P.: 1973,Nature Physical Sci. 244, 96.
Tafel, J.: 1973,Phys. Letters 45A, 241.
Thorne, K. S.: 1967,Astrophys. J. 148, 51.
Trautman, A.: 1972,Bull. Acad. Pol. Sci., Sér. Sci. Math., Astron. Phys. 20, 185, 503, 895.
Trautman, A.: 1973, Istituto Nazion. Alta Matem.,Symposia Matematica 12, 139.
Uhlenbeck, G. E. and Goudsmit, S.: 1925,Naturwissenschaften 13, 953.
Vajk, J. P.: 1969,J. Mathematical Phys. 10, 1145.
Vajk, J. P. and Eltgroth, P. G.: 1970,J. Mathematical Phys. 11, 2212.
Von der Heyde, P.: 1973, Diploma Thesis, Clausthal, Techn. Univ.
Von der Heyde, P.: 1975,Gravitation in Microphysics, preprint.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kuchowicz, B. Some cosmological models with spin and torsion, I. Astrophys Space Sci 39, 157–172 (1976). https://doi.org/10.1007/BF00640517
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00640517